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 A296009 Smallest number m such that (2n-1)*m has only odd digits. 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 5, 3, 5, 11, 1, 1, 1, 1, 1, 13, 13, 3, 11, 11, 1, 1, 1, 1, 1, 13, 5, 3, 5, 11, 1, 1, 1, 1, 1, 17, 11, 7, 11, 11, 1, 1, 1, 1, 1, 11, 5, 3, 5, 11, 1, 1, 1, 1, 1, 11, 11, 3, 11, 15, 1, 1, 1, 1, 1, 11, 5, 11, 5, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS Record values: 1 * 1 = 1 21 * 15 = 315 81 * 17 = 1377 167 * 19 = 3173 169 * 33 = 5577 201 * 155 = 31155 633 * 283 = 179139 1011 * 743 = 751173 1101 * 833 = 917133 2001 * 1555 = 3111555 9091 * 4309 = 39173119 9901 * 32231 = 319119131 91001 * 34193 = 3111597193 100011 * 37927 = 3793117197 101001 * 58553 = 5913911553 200001 * 155555 = 31111155555 909091 * 431109 = 391917311919 990001 * 12121113 = 11999913991113 999001 * 31222311 = 31191119911311 ... (above are exhaustive) 99990001 * 31122223111 = 3111911119991113111 (verified smallest) 9999900001 * 31112222231111 = 311119111119999111131111 (not verified smallest) LINKS Yang Haoran, Table of n, a(n) for n = 1..10001 FORMULA a(n) = A061808(n)/(2n-1). EXAMPLE For n = 11, 2n-1 = 21, 21*15 = 315 which has all odd digits. For m = 1 to 14, n*m listed are 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, all of which contains at least one even digit. MATHEMATICA f[n_] := Block[{m = 1, nn = 2n -1, od = {1, 3, 5, 7, 9}}, While[ Union@ Join[od, IntegerDigits[m*nn]] != od, m += 2]; m]; Array[f, 75] (* Robert G. Wilson v, Dec 05 2017 *) PROG (PARI) isok(n, m) = {my(d = digits((2*n-1)*m)); #select(x->((x%2)==0), d) == 0; } a(n) = {my(m=1); while (!isok(n, m), m++); m; } \\ Michel Marcus, Sep 24 2019 CROSSREFS Cf. A061808, A216473. Sequence in context: A279023 A272682 A111122 * A104436 A070601 A332843 Adjacent sequences:  A296006 A296007 A296008 * A296010 A296011 A296012 KEYWORD base,nonn,look AUTHOR Yang Haoran, Dec 02 2017 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)